I think an important point here is that at the time the Bill of Rights was written, the language you quoted would protect you from having your private information copied. Because without photographs, video, or digital information, you had to actually physically "search" or "seize" a document in order to make a copy of it. There would be no way of copying a document without first getting access to it which, unless the government had a specific warrant, would have been prohibited by the 4th amendment.

Therein lies the problem. The government gets to approach the issue from "It's not explicitly in the Constitution, therefore we can do anything we want," when it is doubtful that the spirit of the document intended peoples digital communications to be handled differently than their physical communication.

IANAL, but here's my interpretation. There are two concerns here:

(1) The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated

and (2) no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.

(1) being the protection, and (2) mentioning the loophole of warrants and protections on that as well. Searching digital information without a warrant violates (1). The legal way to do it is via warrants, and limitations on warrants are prescribed in (2).